What is the AI discipline where an algorithm learns from an initial training set, but then refines its learning as it uses that training?
I believe this can best be done with reinforcement learning via Deep Q Learning. That's where I would start. Steps are:


Initialize a Q table.
Choose an action.
Perform the action.
Measure the reward.
Update the Q.


A neural net will approximate the Q function. See: https://medium.com/emergent-future/simple-reinforcement-learning-with-tensorflow-part-0-q-learning-with-tables-and-neural-networks-d195264329d0

Also consider policy gradients, actor critic, and inverse reinforcement learning.